The problem describes a series combination of two resistors and provides their equivalent resistance. We need to find the value of one of the resistors. For resistors connected in series, the equivalent resistance is the sum of individual resistances.
Correct Option: D) 2 ohm
The question asks about the presence of membrane-bound organelles in different types of cells. To answer this, we need to recall the fundamental differences between prokaryotic and eukaryotic cells regarding their internal organization.
Correct Option: D) Only prokaryotic cells. Prokaryotic cells lack a nucleus and other membrane-bound organelles. This is a key distinguishing feature between prokaryotes and eukaryotes.
The value of \(36^{\frac{1}{6}}\) is:
To find the value of the given expression, we need to simplify the exponential term by expressing the base as a power of a smaller number. We will use the properties of exponents, specifically the rule \((a^m)^n = a^{mn}\).
Correct Option: D) \(6^{\frac{1}{3}}\) is the simplified value of \(36^{\frac{1}{6}}\).
The problem asks us to find the values of X and Y such that the mathematical operation relating the first number to the second number in the pair \(X : 192\) is the same as the operation relating the first number to the second number in the pair \(34 : Y\). We need to test the given options to find the consistent pattern.
D) X = 59, Y = 117
The pattern is that the second number is obtained by multiplying the first number by 3 and then adding 15.
The question asks to identify which of the given animals exhibits the power of regeneration. Regeneration is the biological process by which an organism regrows lost or damaged body parts. We need to recall the regenerative capabilities of each animal listed in the options.
C) Planaria — Planaria are famous for their exceptional regenerative capabilities. They can regenerate a complete organism from even a small fragment of their body, making them a prime example of an animal exhibiting high regenerative power.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to find the relationship between the letters in each pair based on their positions in the English alphabet.
Based on this analysis, Option B (XF-SC) is the one that does not follow the pattern, as the difference between the letters in its clusters is 8 and 10, respectively, unlike the other options where the difference is consistently 10 for both clusters in the pair.
B) XF-SC. In this option, for the cluster XF, the cyclic difference from X to F is \(26 - 24 + 6 = 8\). For the cluster SC, the cyclic difference from S to C is \(26 - 19 + 3 = 10\). Since the differences (8 and 10) are not the same, this pair does not belong to the group.
The question asks for the specific date on which the Department of Posts launched its philately scholarship scheme in 2024. This is a factual recall question related to current affairs or government initiatives.
Correct Option: B) 24 August 2024 — The Department of Posts officially launched the Deen Dayal SPARSH Yojana, a philately scholarship scheme, on August 24, 2024.
This problem involves setting up a system of linear equations based on the given age relationships and then solving for the required difference. We will assign variables to the ages of the individuals mentioned and translate each statement into an equation.
Let Amrita's age be \(x\) years.
Let Amita's age be \(A\) years.
Let Amita's father's age be \(F\) years.
Let Amrita's sister's age be \(S\) years.
From Equation 2, substitute \(A\) from Equation 1 into Equation 2:
\[ F = 2(x + 2) = 2x + 4 \quad \text{(Equation 5)} \]From Equation 3, express \(S\) in terms of \(x\):
\[ S = \frac{x}{2} \quad \text{(Equation 6)} \]Now, substitute Equation 5 and Equation 6 into Equation 4:
\[ (2x + 4) - \left(\frac{x}{2}\right) = 43 \]Multiply the entire equation by 2 to eliminate the fraction:
\[ 2(2x + 4) - x = 2(43) \]\[ 4x + 8 - x = 86 \]\[ 3x + 8 = 86 \]\[ 3x = 86 - 8 \]\[ 3x = 78 \]\[ x = \frac{78}{3} \]\[ x = 26 \]Amrita's age (\(x\)) = 26 years.
Amita's age (\(A\)) = \(x + 2 = 26 + 2 = 28\) years.
Difference = Amita's age - Amrita's age
Difference = \(28 - 26 = 2\) years.
A) The difference between the ages of Amita and Amrita is 2 years, which matches our calculation. This is directly stated in the first line of the problem and confirmed by our calculations.
To find the median when the mean and mode are given, we use the empirical relationship between the mean, median, and mode for a moderately skewed distribution. The empirical formula states that:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] We can rearrange this formula to solve for the median.
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
\[ 23 = 3 \times \text{Median} - 2 \times 65 \]
\[ 23 = 3 \times \text{Median} - 130 \]
Add 130 to both sides of the equation:
\[ 23 + 130 = 3 \times \text{Median} \]
\[ 153 = 3 \times \text{Median} \]
Divide both sides by 3:
\[ \text{Median} = \frac{153}{3} \]
\[ \text{Median} = 51 \]
Correct Option: B) 51
The question asks for the venue of the final match of the Irani Trophy 2024-25, which was won by Mumbai. To answer this, one needs to recall current events and sports news related to Indian domestic cricket.
C) Lucknow is the correct answer. The final match of the Irani Trophy 2024-25, where Mumbai emerged victorious, was indeed held at the Bharat Ratna Shri Atal Bihari Vajpayee Ekana Cricket Stadium in Lucknow.